arXiv subjects

Aitor Balmaseda

Publications and source records attributed to Aitor Balmaseda.

9 recordsLinked to original sources

arXiv2026

Rotating-wave approximation for spin-boson models with structured fields

We derive state-dependent bounds on the difference between two quantum evolutions generated by unbounded Hamiltonians sharing a common form domain. The main technical tool is a second integration by parts, performed at the level of sesquilinear forms rather than at the operator level, which removes the need for a common invariant operator domain. The resulting estimate involves the norm of the time-integrated difference of the two generators, rather than the integral of its norm, and is therefore sensitive to the averaging effects produced by fast-oscillating terms. As an application we prove a quantitative bound on the rotating-wave approximation for spin-boson models with a structured boson field, described by an arbitrary massive dispersion relation on a general measure space and by a suitable class of form factors. The proof involves a careful analysis of the high-frequency scaling. The bound holds on a dense subspace of states, is fully explicit, and all the constants entering it depend only on the parameters of the model and not on the frequency scale, so that the approximation becomes exact in the limit of large frequency.

math-ph↗

arXiv2025

Distillation of multipartite entangled states for arbitrary subsets of parties in noisy quantum networks of increasing size

Quantum network states are multipartite states built from distributing pairwise entanglement among parties and underpin the paradigm of quantum networks for quantum information processing. In this work we introduce the problem of partial distillability in noisy quantum networks. This corresponds to the possibility of distilling by local operations and classical communication an arbitrary pure state for an arbitrary subset of parties starting from a single copy of a quantum network state of an increasing number of parties that share noisy (i.e. mixed) bipartite entangled states. Here, distillation means that the target state is obtained with fidelity as close to 1 as desired as the size of the network increases when the pairwise entangled links support a constant amount of noise. While we prove an obstruction to multipartite distillation protocols after teleportation with channels with constant noise, we show that partial distillability is indeed possible if certain well-established graph-theoretic parameters that measure the connectivity in the network grow fast enough with its size. We give necessary as well as sufficient conditions for partial distillability in terms of these parameters and we moreover provide explicit constructions of networks with partial distillability and a relatively slow connectivity growth.

quant-ph↗

arXiv2024

Global approximate controllability of quantum systems by form perturbations and applications

We provide sufficient conditions for the approximate controllability of infinite-dimensional quantum control systems corresponding to form perturbations of the drift Hamiltonian modulated by a control function. We rely on previous results on controllability of quantum bilinear control systems and obtain a priori $L^1$-bounds of the controls for generic initial and target states. We apply a stability result for the non-autonomous Schr\"odinger equation to extend the results to systems defined by form perturbations, including singular perturbations. As an application of our results, we prove approximate controllability of a quantum particle in a one-dimensional box with a point-interaction with tuneable strength at the centre of the box.

math.OC↗

arXiv2023

Quantum controllability on graph-like manifolds through magnetic potentials and boundary conditions

We investigate the controllability of an infinite-dimensional quantum system: a quantum particle confined on a Thick Quantum Graph, a generalisation of Quantum Graphs whose edges are allowed to be manifolds of arbitrary dimension with quasi-$δ$ boundary conditions. This is a particular class of self-adjoint boundary conditions compatible with the graph structure. We prove that global approximate controllability can be achieved using two physically distinct protocols: either using the boundary conditions as controls, or using time-dependent magnetic fields. Both cases have time-dependent domains for the Hamiltonians.

math-ph↗

arXiv2023

On a sharper bound on the stability of non-autonomous Schr\"odinger equations and applications to quantum control

We study the stability of the Schr\"odinger equation generated by time-dependent Hamiltonians with constant form domain. That is, we bound the difference between solutions of the Schr\"odinger equation by the difference of their Hamiltonians. The stability theorem obtained in this article provides a sharper bound than those previously obtained in the literature. This makes it a potentially useful tool for time-dependent problems in Quantum Physics, in particular for Quantum Control. We apply this result to prove two theorems about global approximate controllability of infinite-dimensional quantum systems. These results improve and generalise existing results on infinite-dimensional quantum control.

math-ph↗

arXiv2022

Quantum Control at the Boundary

This dissertation presents and prove the viability of a non-standard method for controlling the state of a quantum system by modifying its boundary conditions instead of relying on the action of external fields. The standard approach to quantum control bases on the use of an external field to manipulate the system. Some technological difficulties appear when controlling a quantum system in this way, due to the complications of manipulating a system made of few particles while maintaining the quantum correlations. As a consequence the systems need to be kept at very low temperatures and the interactions have to be performed very fast. The Quantum Control at the Boundary approach is radically different to the standard one. Instead of seeking the control of the quantum system by directly interacting with it through an external field, the control is achieved by manipulating the boundary conditions of the system. The spectrum of a quantum system, for instance an electron moving in a box, depends on the boundary conditions imposed on it. Hence, a modification of such boundary conditions modifies the state of the system allowing for its manipulation and, eventually, its control. This kind of interaction is weaker, which makes one to expect that it may help maintaining the quantum correlations. For showing the viability of the Quantum Control at the Boundary method, a family of boundary control systems on Quantum Circuits (a generalization of quantum grahs) is introduced. Before being able to address the problem of controllability, the problem of existence of solutions for the Schrödinger equation with time-dependent boundary conditions is addressed. The approximate controllability of the systems under study is proven using a controllability result by T. Chambrion et al. (2009) and a stability result which constitutes another original contribution of this dissertation.

math-ph↗

arXiv2022

On global approximate controllability of a quantum particle in a box by moving walls

We study a system composed of a free quantum particle trapped in a box whose walls can change their position. We prove the global approximate controllability of the system. That is, any initial state can be driven arbitrarily close to any target state in the Hilbert space of the free particle with a predetermined final position of the box. To this purpose we consider weak solutions of the Schrödinger equation and use a stability theorem for the time-dependent Schrödinger equation.

math.OC↗

arXiv2022

On the Schrödinger Equation for Time-Dependent Hamiltonians with a Constant Form Domain

We study two seminal approaches, developed by B. Simon and J. Kisyński, to the well-posedness of the Schrödinger equation with a time-dependent Hamiltonian. In both cases the Hamiltonian is assumed to be semibounded from below and to have constant form domain but a possibly non-constant operator domain. The problem is addressed in the abstract setting, without assuming any specific functional expression for the Hamiltonian. The connection between the two approaches is the relation between sesquilinear forms and the bounded linear operators representing them. We provide a characterization of continuity and differentiability properties of form-valued and operator-valued functions which enables an extensive comparison between the two approaches and their technical assumptions.

math.FA↗

arXiv2019

Quantum Control at the Boundary: an application to quantum circuits

Approximate controllability for a quantum system on a graph using as control parameters boundary conditions will be proven. This establishes a first theoretical proof of the feasibility of the quantum control at the boundary paradigm. A simplified version of this results can be found in arXiv:1811.09541.

math-ph↗